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A284600 a(n) = n/(largest prime power dividing n).

%I A284600 #21 Apr 29 2021 12:32:48
%S A284600 1,1,1,1,1,2,1,1,1,2,1,3,1,2,3,1,1,2,1,4,3,2,1,3,1,2,1,4,1,6,1,1,3,2,
%T A284600 5,4,1,2,3,5,1,6,1,4,5,2,1,3,1,2,3,4,1,2,5,7,3,2,1,12,1,2,7,1,5,6,1,4,
%U A284600 3,10,1,8,1,2,3,4,7,6,1,5,1,2,1,12,5,2,3,8,1,10
%N A284600 a(n) = n/(largest prime power dividing n).
%C A284600 a(n) = smallest positive number k such that n/k is a prime power.
%H A284600 Robert Israel, <a href="/A284600/b284600.txt">Table of n, a(n) for n = 1..10000</a>
%H A284600 Ilya Gutkovskiy, <a href="/A284600/a284600.pdf">Extended graphical example</a>
%F A284600 a(n) = n/A034699(n).
%F A284600 a(n) = 1 if n is a prime power (A000961).
%F A284600 a(n) = 2 if n is a twice odd prime power (A278568).
%e A284600 a(12) = 3 because 12 = 2^2*3 therefore 12/(largest prime power dividing 12) = 12/4 = 3.
%p A284600 f:= n ->  n /max(map(t -> t[1]^t[2], ifactors(n)[2])):
%p A284600 f(1):= 1:
%p A284600 map(f, [$1..100]); # _Robert Israel_, Apr 09 2017
%t A284600 Join[{1}, Table[n/Last[Select[Divisors[n], PrimePowerQ[#1] &]], {n, 2, 90}]]
%o A284600 (Python)
%o A284600 from sympy import lcm
%o A284600 def a003418(n): return 1 if n<1 else lcm(range(1, n + 1))
%o A284600 def a(n):
%o A284600     m=1
%o A284600     while True:
%o A284600         if a003418(m)%n==0: return m
%o A284600         else: m+=1
%o A284600 print([n//a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Apr 04 2017
%Y A284600 Cf. A000961, A003557, A007913, A034699, A052126, A121289, A278568.
%Y A284600 Has same beginning as A052128 and A114536 but is strictly different from those two sequences.
%K A284600 nonn
%O A284600 1,6
%A A284600 _Ilya Gutkovskiy_, Mar 30 2017